Integrated Modeling and Design of Photoelectrochemical Water-Splitting Cells By Alan Day Berger ...

109 Pages·2014·2.49 MB·English

by  Alan Berger

Integrated Modeling and Design of Photoelectrochemical Water-Splitting Cells

By
Alan Day Berger

A dissertation submitted in partial satisfaction of the
requirements for the degree of
Doctor of Philosophy
in
Chemical Engineering
in the
Graduate Division
of the
University of California, Berkeley

Committee in charge:
Professor John Newman, Chair
Professor Rachel Segalman
Professor Costas Grigoropoulos

Spring 2014

Abstract
Integrated Modeling and Design of Photoelectrochemical Water-Splitting Cells
by
Alan Day Berger
Doctor of Philosophy in Chemical Engineering
University of California, Berkeley
Professor John Newman, Chair

The photoelectrochemical production of fuels is an interesting research topic that aims to provide
a low-cost method for storing solar energy. A one-dimensional model of a photoelectrochemical
cell for solar water splitting has been developed, with applicability to both wired and wireless
designs. The model of the light absorber handles electron and hole transport. The model of the
electrolyte accounts for mass transport through regions of aqueous solution, including stagnant
diffusion layers and bulk regions to address mixing due to bubbles, natural convection, or other
sources. A polymer membrane may be present in the electrolyte.
The models of the light absorber and the electrolyte are integrated through the reactions taking
place at the interface between them. Charge transfer from the semiconductor to the solution is
handled using a kinetic model involving reactions between the species in both the light absorber
and the electrolyte. A simplified model is also presented for use when concentration gradients in
the electrolyte are negligible. The simplified model captures the effect of the electrolyte in the
boundary conditions for the light-absorber.
Throughout, the model is validated against experimental data. At the outset, simulated output
compares favorably with current-potential data for a hydrogen-evolving light absorber with
varying degrees of simulated solar illumination. Later, the program is able to match current-
potential data and bulk pH values for a membrane electrolysis cell with several electrolytes.
The model is first used to study the effect of changing the electrolyte on the performance of a
photoelectrochemical cell. It is discovered that using supported dilute acids or buffered
electrolytes in an attempt to work in near-neutral conditions is ineffective. Cells with neutral
electrolytes cannot run at high current density due to transport limitations in the electrolyte and
solubility limitations that are encountered due to electrodialysis.
Later, an absorber-in-membrane design for a photoelectrochemical cell is considered. Gas
crossover is identified as a significant issue in these systems, and metrics are developed for
evaluating system performance properly. Material targets are established. For instance,
membranes with ten times the gas-blocking properties of currently available polymers (i.e.,
Nafion) are desired.
1
Contents

List of Figures ................................................................................................................................ iii
List of Tables .................................................................................................................................. v
Acknowledgements ........................................................................................................................ vi

1. Introduction ............................................................................................................................. 1
1.1. Solar Fuels ........................................................................................................................ 1
1.2. Photoelectrochemical cells ............................................................................................... 2
1.3. Approach .......................................................................................................................... 5
1.4. References ........................................................................................................................ 6

2. Integrated model of a Photoelectrochemical Cell ................................................................. 10
2.1. Introduction .................................................................................................................... 10
2.2. Cell geometry ................................................................................................................. 11
2.3. Governing Equations for Light Absorber....................................................................... 15
2.3.1. Boundary Conditions for Light Absorber ............................................................... 17
2.4. Governing Equations for Electrolyte.............................................................................. 21
2.5. Boundary conditions ...................................................................................................... 23
2.5.1. Boundary conditions for electrolyte/anode interface .............................................. 23
2.5.2. Boundary conditions for electrolyte/cathode interface ........................................... 25
2.5.3. Internal boundary conditions for electrolyte/membrane interface .......................... 26
2.6. Integrated Model with Simplified Electrolytic Transport .............................................. 26
2.7. Full Integrated Model ..................................................................................................... 29
2.7.1. Solution methods and parameters ........................................................................... 31
2.7.2. Experimental validation .......................................................................................... 31
2.8. References ...................................................................................................................... 33

3. Impact of Electrolyte pH on Photoelectrochemical Cell Performance ................................. 37
3.1. Approach ........................................................................................................................ 37
3.2. Contributions to the cell potential .................................................................................. 37
i
3.3. Comment on electrolyte pH ........................................................................................... 39
3.3.1. Solution composition at equilibrium ....................................................................... 40
3.3.2. Solution composition when passing current ........................................................... 40
3.4. Diffusion layers and mixing ........................................................................................... 41
3.5. Current due to shuttling of buffer species ...................................................................... 47
3.6. Cell potential .................................................................................................................. 51
3.6.1. Experimental validation .......................................................................................... 51
3.7. Model results for dilute acid with supporting electrolyte .............................................. 53
3.8. Model results for buffer electrolyte ................................................................................ 60
3.9. Solution pH .................................................................................................................... 62
3.9.1. Model results for dilute acid with supporting electrolyte ....................................... 62
3.9.2. Model results for buffer electrolyte ........................................................................ 64
3.10. Efficiencies and gas purity ......................................................................................... 68
3.11. Conclusions ................................................................................................................ 71
3.12. References .................................................................................................................. 71

4. Analysis of Absorber-in-Membrane Configuration for Photoelectrochemical Cells ........... 74
4.1. Introduction .................................................................................................................... 74
4.2. System description ......................................................................................................... 75
4.3. Effect of crossover: numerical solution with PEC model .............................................. 79
4.3.1. Net hydrogen collected and true efficiency of a PEC ............................................. 79
4.3.2. Trade-off between high conductivity and low permeability ................................... 83
4.3.3. Limits on the benefit of reducing permeability....................................................... 86
4.4. Effect of crossover: simplified semi-analytical solution ................................................ 89
4.5. Effect of absorber efficiency .......................................................................................... 91
4.6. Effect of absorber area fraction ...................................................................................... 95
4.7. Summary of absorber-in-membrane model.................................................................... 96
4.8. References ...................................................................................................................... 98

ii
List of Figures

Figure 1-1: ASTM Reference Solar Spectrum: Air Mass 1.5 Global (AM 1.5G) .......................... 4

Figure 2-1: The planar photoelectrochemical cell in the “wired” configuration. ......................... 12
Figure 2-2: 2-D projection of the “wireless” or “absorber-in-membrane” design. ....................... 13
Figure 2-3: General 1-D model geometry. .................................................................................... 14
Figure 2-4: Diagram of the surface model. ................................................................................... 17
Figure 2-5: BAND diagram for the equations and boundary conditions in the simplified
integrated model.......................................................................................................... 28
Figure 2-6: BAND diagram for the equations and boundary conditions in the full integrated
model........................................................................................................................... 30
Figure 2-7: Comparison of model output to experimental data. ................................................... 33

Figure 3-1: Geometry for the 1-D model. ..................................................................................... 37
Figure 3-2: Impact of diffusion layer thickness, HClO . .............................................................. 44
4
Figure 3-3: Impact of diffusion layer thickness, HClO , low current. .......................................... 44
4
Figure 3-4: Impact of diffusion layer thickness, H SO . .............................................................. 45
2 4
Figure 3-5: Dependence of limiting current density on thickness of diffusion layer,
HClO /NaClO ............................................................................................................ 46
4 4
Figure 3-6: Dependence of limiting current on thickness of diffusion layer, H SO /K SO . ...... 47
2 4 2 4
Figure 3-7: Schematic for division of current between protons and buffer species. .................... 48
Figure 3-8: Current carried by protons and buffer species versus position. ................................. 49
Figure 3-9: Division of current between protons and buffer species, no membrane. ................... 50
Figure 3-10: Division of current between protons and buffer species, Nafion membrane. .......... 51
Figure 3-11: Experimental validation of the model. ..................................................................... 53
Figure 3-12: Simulated load curves for dilute HClO at selected pH values................................ 54
4
Figure 3-13: Simulated load curves for dilute H SO at selected pH values. ............................... 55
2 4
Figure 3-14: Simulated load curves for HClO supported with NaClO . ..................................... 56
4 4
Figure 3-15: Simulated load curves for H SO supported with K SO . ....................................... 57
2 4 2 4
Figure 3-16: Comparison of potential losses for HClO at pH 1.5. .............................................. 59
4
Figure 3-17: Comparison of potential losses for supported HClO at pH 1.5. ............................. 60
4
iii
Figure 3-18: Current-potential relationships for a buffer electrolyte. ........................................... 61
Figure 3-19: Components of the cell potential for a borate buffer electrolyte. ............................ 62
Figure 3-20: Magnitude of pH swing. ........................................................................................... 63
Figure 3-21: Experimental data (asterisks) and model predictions for the bulk pH ..................... 64
Figure 3-22: Concentration and pH effects for the buffered system of Figure 3-18 with an AEM.
..................................................................................................................................... 66
Figure 3-23: Concentration profiles in the diffusion layer near the cathode, borate buffer. ........ 67
Figure 3-24: Plot of pH at different locations as a function of current density. ........................... 67
Figure 3-25: a) Efficiency of the cells from Figure 3-2 at a current density of 10 mA/cm2. ....... 68
Figure 3-26: Efficiency of the cells from Figure 3-2 at a current density of 1 mA/cm2. .............. 69
Figure 3-27: Efficiency of the cell from Figure 3-2 with 100 µm diffusion-layer thickness as a
function of current density. ......................................................................................... 69
Figure 3-28: Amount of impurity in exit streams. ........................................................................ 70

Figure 4-1: Absorber-in-membrane geometry. ............................................................................. 76
Figure 4-2: The effect of crossover on the load curve. ................................................................. 80
Figure 4-3: Total current and net H collected versus length. ...................................................... 81
2
Figure 4-4: Effect of catalyst activity. .......................................................................................... 83
Figure 4-5: Effect of relative humidity (RH). ............................................................................... 84
Figure 4-6: Relative variation of permeability and conductivity .................................................. 85
Figure 4-7: Net hydrogen produced as a function of conductivity. .............................................. 86
Figure 4-8: Effect of permeability on net H collected as a function of thickness. ...................... 87
2
Figure 4-9: Effect of permeability on maximum current and net H . ........................................... 88
2
Figure 4-10: Simplified tradeoff between ion and gas transport – varying relative humidity. ..... 90
Figure 4-11: Simplified tradeoff between ion and gas transport – varying length. ...................... 91
Figure 4-12: Computed absorber and load curves for selected minority-carrier lifetimes. .......... 93
Figure 4-13: Effect of recombination kinetics on light-absorber efficiency. ................................ 94
Figure 4-14: Effect of wire area ratio. .......................................................................................... 96

iv
List of Tables

Table 2-1: Area ratios and geometric constraints* ....................................................................... 14
Table 2-2: Material properties and kinetic parameters for light absorber model.* ...................... 31
Table 2-3: Model parameters for the electrolyte. .......................................................................... 32

Table 3-1: Model parameters and physical properties .................................................................. 42
Table 3-2: Model parameters for dilute and supported H SO data ............................................. 52
2 4
Table 3-3: Limits on current density due to solubility* ................................................................ 65

Table 4-1: List of material properties and geometric ratios. ......................................................... 78
Table 4-2: Effect of crossover on current and net hydrogen collected. ........................................ 80

v
Acknowledgements
First and foremost, I must thank Professor Newman for his guidance and mentorship. His
commitment to his students' understanding and wellbeing is second to none. He takes the time to
answer scientific questions in detail. In every conversation, he is very careful to point out the
nuances in how different topics are related. He teaches his students to appreciate the full
complexity of a problem, but he also helps them see the beauty in reducing the larger problem to
a simple but adequate description. Furthermore, he never fails to provide adequate perspective
for any discussion. His valuable insights extend far beyond the realm of science and
electrochemistry, and I am truly appreciative of all of the lessons he imparted, both technical and
nontechnical.
My graduate school career at Berkeley has been a true blessing, and I owe a great deal of thanks
to my colleagues and friends throughout the past five years. My labmates in the Newman Group,
including Lisa Onishi, Ryan Balliet, Haluna Gunterman, Maureen Tang, Nathan Craig, and
Anthony Ferrese, made it an absolute pleasure to work in 301-B Gilman Hall. They also
provided many fond memories outside the confines of academia.
I also had the good fortune to work with many excellent researchers at the Joint Center for
Artificial Photosynthesis, and there are too many individuals to list my appreciation for each one
of them. I hope I have expressed it adequately in person. In particular, advice from Rachel
Segalman, Carl Koval, and Adam Weber has been appreciated. Working with Miguel
Modestino, Karl Walczak, Sophia Haussener, Christopher Evans, and Daniel Miller has been
very fruitful and enjoyable. My roommates and my classmates have made many positive
memories that I will always cherish.
I also thank my family, especially my parents, Rosanne and Dave, and my sister, Alta, for their
loving support. This journey would not have been possible without the foundation they built for
me and their continued encouragement.
Maureen Tang, my wife, is the newest member of my family and bears special recognition.
Because we worked together, she is mentioned twice (and rightfully so). I surely underestimate
the number of sacrifices Maureen and the rest of my family have made on my behalf. I will
always strive to make them happy and proud.
Finally, I gratefully acknowledge funding support from the U.S. DOE through the Joint Center
for Artificial Photosynthesis.

vi
1. Introduction

1.1. Solar Fuels
Research in solar fuels is motivated by energy concerns. Global consumption of energy
reached 17.5 TW in 2010 and continues to rise.1 Meeting this demand with the known reserves
of different fuel types will be challenging. The exhaustion times of various resources such as
coal, oil, natural gas, and uranium for nuclear power are all on the order of tens or hundreds of
years (with considerable uncertainty).2 There have been attempts to bring various renewable
energy sources to scale, but they still represent only about 10% of the energy market in the
United States. To three significant figures, domestic production and consumption of renewable
energy are both equal to 0.31 TW, and therefore they account for only 11.4% of U.S. energy
production and 9.5% of U.S. energy consumption in 2013 according to the Energy Information
Administration.3 Approximately half of renewable consumption is due to biomass, and the top
contributors are wood at 71 GW and biofuels (ethanol and biodiesel) at 67 GW. The next largest
contributor is hydroelectric power at 86 GW, with wind and solar accounting for only 53 GW
and 10 GW, respectively.
Utilizing the solar resource more fully is attractive due to its sheer capacity of 85 PW
globally.4 However, the intermittency of the solar energy means that energy storage will be
necessary. It is preferable to store energy in molecular bonds as a fuel rather than store electrical
energy in a battery. This is true because the superior specific energy of fuels (especially liquid
fuels) leads to lower costs, especially when the energy needs to be stored for longer than a day.5
For the same reasons, fuels are well-suited for transportation applications, which account for
28% of energy consumption in the United States.3
We have established that conversion of sunlight, water, and carbon-containing sources
into fuels is an appealing goal. This process is sometimes called "artificial photosynthesis," and
it has attracted a great deal of recent research.6–8 The overall process can be roughly described in
the following way:
( 1-1)

Here, the product would be some type of useful fuel, and oxygen is a by-product.

One common way to approach this problem is to take an electrochemical route. This
separates the overall reaction between two electrodes where oxidation and reduction take place.
Water can be oxidized at an anode, producing protons and oxygen gas:
( 1-2a)

or alternatively in base:
1